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Barkhausen Demodulation BARKHAUSEN DEMODULATION B. R. Ortquist D. T. Hayford Engineering Physics Group Battelle Memorial Institute 505 King Avenue Columbus, OH 43201 INTRODUCTION A careful examination of the magnetization of a ferromagnetic material reveals that it is a discontinuous process; when subject to a varying magnetic field, a ferromagnetic material is magnetized in discrete bursts as domain boundaries overcome pinning at defects in the crystal lattice. This discrete behavior manifests itself as high frequency "noise" superimposed upon a measurement of magnetic flux and is commonly referred to as the Barkhausen Effect. Several important microstructural properties of steel also depend on lattice defect structure, i. e., mechanical hardness, ferrite content, material fatigue, and internal stress state, and investigators have successfully correlated Barkhausen Effect parameters with these properties [1-3]. Unfortunately, Barkhausen noise signals are broadband and weak, characteristics that often limit the utility of the Barkhausen Effect in NDE applications. In this paper, we will describe a phenomenon we call Barkhausen Demodulation, which provides a means of measuring Barkhausen noise that lends itself more readily to NDE investigations. Further, we will describe an experiment in which Barkhausen Demodulation was used to measure the hardness of X40 grade pipeline steel. BACKGROUND In the mid 18oos, an intellectually eclectic dentist by the name of Mahlon Loomis discovered that an amplitude modulated, high frequency electromagnetic field can be demodulated using a ferromagnetic pickup subject to a slowly varying magnetic field [4]. From this observation, he was able to develop a receiver capable of demodulating amplitude-modulated RF radiation, and subsequently, to demonstrate the world's first wireless telegraphy device. For this invention, Loomis was granted a patent in 1872. The phenomenon that he exploited, sometimes called the Loomis Effect, could not be explained in his day - it would depend on Barkhausen's discovery of his eponymous effect circa 1918. What follows is a qualitative explanation of the Loomis Effect, which we have chosen to call by the more descriptive name of Barkhausen Demodulation. First, however, a brief discussion of the mechanisms of magnetic domain growth and the Barkhausen Effect is in order. THE BARKHAUSEN EFFECT The dynamics of magnetic domain growth is largely responsible for the colorful magnetic behavior - hysteresis, the Barkhausen Effect, and other non-linear phenomena - exhibited by a ferromagnetic material under the influence of a magnetic field. Domain growth can be classified into three types: reversible domain wall displacements, irreversible domain wall displacements, and reversible domain rotations. Reversible domain wall displacements occur for an initially unmagnetized sample subjected to a small magnetic field. In this type of domain growth, domain wall motions proceed unimpeded such that domains oriented in the direction of easy magnetization nearest to that of the applied field (favorably aligned domains) are increased in size while domains of other orientations remain unchanged or are decreased in size. Because the domain motions are unimpeded, a cyclical change in field will cause no net change in magnetization, thus this type of domain growth is reversible. Review ofProgress in Quantitative Nondestructive Evaluation. Vol. 14 Edited by D.O. Thompson and D.E. Chimenti. Plenum Press, New York, 1995 1709 Irreversible domain wall displacements occur for intermediate applied fields (and for small fields when the sample is magnetized). In this type of domain growth, domain wall motions proceed unimpeded until domain walls become pinned at impurities or discontinuities in the crystal lattice. As the applied field is further increased in magnitude, pinned domain walls eventually acquire enough energy to overcome pinning and domain growth resumes until the next pinning sites are encountered. As a result, domain growth occurs in bursts as favorably aligned domains increase in size and those unfavorably aligned remain unchanged or decrease in size following each pinning break. This discrete character of the magnetization is known as the Barkhausen Effect and each pinning break is called a Barkhausen Event. Because of the quantized character of the Barkhausen Events, a cyclical change in field will not, in general, leave the magnetization unchanged, thus this type of domain growth is irreversible. Reversible domain rotations occur for large applied fields after favorably aligned domains have grown to the limits imposed by crystalline boundaries. In this type of domain growth (though, here, "growth" is a misnomer), the magnetization of the sample increases in the direction of the applied field as the individual dipole moments comprising favorably aligned domains rotate into this direction. If the magnitude of the applied field is subsequently reduced, the dipole moments will rotate back into the domain direction (the most favorably aligned direction of easy magnetization), thus, this type of domain growth is reversible. Figure 1 shows a typical magnetization curve for a ferromagnetic material. Regions of the curve in which each of the three types of domain growth dominate are marked on the figure. Also, a portion of the curve lying in the region dominated by irreversible domain wall displacements has been blown up to illustrate the discrete nature of magnetization associated with the Barkhausen Effect. BARKHAUSEN DEMODULATION For the following discussion, we will adopt a very simple model of an iron-based material that is useful for illustrating domain growth when the material is subject to an external magnetic field. Figure 2a depicts the model, in which four of the easy directions of magnetization are considered, denoted ±yand ±z, with one domain oriented in each direction (ferritic steel has a cubic crystal structure and, thus, in reality, has six easy directions). A pinning site has been located at the point of intersection of the domain walls. Though this is a simplistic model, the arguments that follow can easily be generalized beyond these assumptions. If the specimen is subjected to a slowly increasing magnetic field in the +z direction, Hz, domains oriented in this direction will grow at the expense of domains less favorably oriented, especially those oriented in the -z direction. Domain growth will continue in this manner until domain walls become pinned. Figure 2b shows the domain wall displacements resulting from the application of liz. As indicated in the figure, domain walls A and D shift such that the +z domain increases in size, while the movements of domain walls B and C cause the -z domain to decrease in size. The sizes of the +y and -y domains remain roughly unchanged. B reversible domain rotations reversible domain wall displacements irreversible domain wall displacements --------------------~~---------------------H Barkhausen events Figure 1. Magnetization curve for a ferromagnetic material. The curve is divided into regions according to the dominant form of domain growth occurring in each region. A portion of the curve is blown up to indicate the discrete character of magnetization associated with the Barkhausen Effect. 1710 (a) ... ·pinning site (e) (d) t Hz ~f... Hz Hy- Hy - (f) (g) t Hz ~J, -Hy -Hy Figure 2. a. Pictorial magnetic domain model illustrating absolute value effect. Domain orientations are indicated by arrows and domain walls separating domains are labeled A-D. A pinning site is located at the intersection of the four domains. b. Domain wall displacements (solid lines) resulting from the application of liz. c. Domain wall displacements resulting from the application of By oriented in the +y direction. The dashed lines indicate the previous domain wall positions. d. Resulting domain sizes after walls A and C overcome pinning showing that the +z domain has grown. e. Same as (b). f. Domain wall displacements resulting from the application of By oriented in the -y direction. g. Resulting domain sizes after walls B and D overcome pinning showing that the + z domain has again grown. If, in addition to liz, a high frequency, low amplitude AC field is added along the y axis, the resulting domain wall displacements tend to oppose certain displacements caused by Hz and enforce others. Here, two cases must be considered, corresponding to the two orientations of By. First, when By points in the +y direction, domain walls A and C are further stressed whereas domain walls B and D are relaxed slightly. This situation is depicted in Figure 2c where the dashed lines represent the former domain wall positions. Ultimately, the additional energy imparted to domain walls A and C by By will be sufficient to break the pinning of these walls. At the same time, the slight reduction of energy of domain walls B and D will prevent these walls from overcoming pinning. The net result is that the +z and +y domains increase in size at the expense of the -z and -y domains (Figure 2d). In the second case, By points in the -y direction. As indicated in Figure 2f, it is the motions of domain walls B and D that are augmented by By and those of domain walls A and C that are opposed. Hence, in this case, it is domain walls B and D that overcome pinning, and domain walls A and C that do not. Accordingly, the +z and -y domains grow, while the -z and +y domains are depleted (Figure 2g). In summary, regardless of the orientation of By, the magnetization of the sample increases in the +z direction. The steel
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